《平立定三差详说》的一点注记  

A Note on The Detailed Explanation of Pingliding Sancha Fa

作　　者：李兆华[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《中国科技史杂志》2014年第3期281-288,共8页The Chinese Journal for the History of Science and Technology

基　　金：国家自然科学基金(项目编号:11001199)

摘　　要：根据梅文鼎《平立定三差详说》(1704年)的垛积知识导出太阳积差公式(盈积),并指出顾观光《平立定三差解》(1849年)算法的失误。就《授时历》(1280年)平立定三差法的垛积意义给出正确的解释,为积差公式的推导提供了依据,是《平立定三差详说》的重要贡献。Based on information about Duoji Shu （ method for finding the sum of finite series） contained in the work Detailed Explanation of Pingliding Sancha Fa （interpolation, 1704） by Mei Wending （1633 - 1721 ）, this paper establishes the interpolation polynomical. Furthermore, it enquires into a related work, Remarks on Pingliding Sancha Fa （1849）, by Gu Guanguang （1799 1862）, who didn＇t think much of Mei＇s explanation. This paper holds that a great contribution in Mei＇s work is the structure analysis of the interpolation polynomical using Duoji Shu, from which the polynomical is easy to establish, even though how to establish it is not recorded in Mei＇s work. A mistake in mathematical logic made by Gu in his work is also pointed out in the paper.

关 键 词：梅文鼎 《平立定三差详说》 垛积术 积差公式 

分 类 号：N092[自然科学总论—科学技术哲学] O119[理学—数学]